1. SP 2015 17 Lesson B

2. Sampling Distribution Model Sampling models are what make Statistics work. Shows how a sample proportion varies from sample to sample They act as a bridge from the sample data we know to the population truths we wish we knew.

3. Standard Deviation of the Proportion of Successes

4. Assumptions & Conditions Check: Upper Bound for sample size: n ≤ 10% of population Lower Bound for sample size: np ≥ 10 and nq ≥ 10 Assume: For this class, we will assume all samples are Binomial Independent Random

5. Margin of Error How far off our estimate might be

6. Standard Error Estimate of the standard deviation of a sampling distribution. Notice: uses p-hat and q-hat from a sample Standard Deviation used p and q from the population

7. 95% Confidence Interval for a Proportion CI ( lower bound, upper bound

8. Talk the Talk When describing the confidence interval Formally, what we mean is that “95% of samples of this size will produce confidence intervals that capture the true proportion.” Often we say: “We are 95% confident that the true proportion lies in our interval.”

9. Example – Margin of Error On January 30–31, 2007, Fox News/Opinion Dynamics polled 900 registered voters nationwide. When asked, “Do you believe global warming exists?” 82% said “Yes.” Fox reported their margin of error to be 3%. Remember: It is standard among pollsters to use a 95% confidence level unless otherwise stated. What does Fox News mean by claiming a margin of error of 3% in this context? If this polling were done repeatedly, 95% of all random samples would yield estimates that come within 3% of the true proportion of all registered voters who believe that global warming exists.

10. Certainty vs. Precision The margin of error for a 95% confidence interval is 2 SE. What if we wanted to be more confident?  We would need to capture p more often  To do that we’ll need to make the interval wider.  Example, if we want to be 99.7% confident, the margin of error will have to be 3 SE. Of course, we can make the margin of error large enough to be 100% confident, but that isn’t very useful

11. Certainty vs. Precision Larger Margins of Error allow for more confidence Smaller Margins of Error allow for more precision Every confidence interval is a balance between certainty and precision.

12. How helpful would this forecast be?

13. Critical Values We use 2* SE to give us a 95% confidence interval To change the confidence level, we’d need to change the number of SE’s so that the size of the margin of error corresponds to the new level This number of SE’s is called the critical value. We are using the normal model so we denote it: Critical Value = z* We will use z* = 2 from the 68 – 95 – 99.7 rule Technically, z* = 1.96

14. Margin of Error